Are you asking if this is correct? Yes, it is grammatically correct and is included as such. How long someone would live making it a habit to "sleep at the steering wheel" is another question.
Well, the translation given agrees with the original present (continuous) tense while your suggestion keeps the 'is' and introduces an adjective, so I'd say there is no need to do that. :)
I'm agreeing with what D_.. has posted. I'd also add that the expression would have to be either..."My uncle fell asleep at the wheel." which it does not say and in addition that this is a rather idiomatic expression in English which doesn't literally meaning sleeping but that someone, *"is not attentive or alert". He is not doing his job or duties but does not really mean he is driving or in a vehicle.
So, just as D_.. points out we wouldn't use it here.
I would say that (in the UK at least) "... is asleep at the [steering] wheel" is the idiomatic phrase and therefore the obvious translation (I just wrote that). Altho "sleeping at the wheel" is grammatically correct, no one would actually say it.
It is of course true that there is a metaphorical meaning of the expression as jaye16 says, but of course that derives from its common literal usage.
Asleep at the wheel should be accepted. Much more common phrasing for English speakers